Understanding Prime and Composite Numbers When studying mathematics, one of the fundamental concepts that students learn is that of prime and composite numbers. In this article, we will delve into the factors of 48, a composite number, and explore the various ways in which it can be broken down into its component parts.

## Contents

## Factors Calculator

Factors of 48 | 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 |

Negative Factors of 48 | -1, -2, -3, -4, -6, -8, -12, -16, -24 and -48 |

Prime Factors of 48 | 2, 3 |

Prime Factorization of 48 | 2 × 2 × 2 × 2 × 3 |

Factors of 48 in Pairs | (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8) |

Negative Pairs Factors of 48 | (-1, -48), (-2, -24), (-3, -16), (-4, -12), and (-6, -8) |

**Prime Numbers**

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Some examples of prime numbers include 2, 3, 5, 7, and 11. Prime numbers are important in mathematics as they are used in many mathematical formulas and algorithms, and are also used in the study of number theory.

**Composite Numbers**

A composite number is a whole number greater than 1 that can be divided evenly by a number other than 1 or itself. In other words, a composite number is not a prime number. Some examples of composite numbers include 4, 6, 8, 9, and 10.

## What are the factors of 48?

The method of calculating the factors of 48 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 48 are the factors of 48.

By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 48 ÷ 1 = 48

This division gives the remainder 0 and so is divisible by 48. So please put them 1 and 48 in your factor list.

1, …. 48

(ii) 48 ÷ 2 = 24

This division gives the remainder 0 and so is divisible by 24. So please put them 2 and 24 in your factor list.

1, 2 …. 24, 48

(iii) 48 ÷ 3 = 16

This division gives the remainder 0 and so is divisible by 16. So please put them 3 and 16 in your factor list.

1, 2, 3 …. 16, 24, 48

(iv) 48 ÷ 4 = 12

This division gives the remainder 0 and so is divisible by 12. So please put them 4 and 12 in your factor list.

1, 2, 3, 4 …. 12, 16, 24, 48

(v) 48 ÷ 5 = 9.6

This division gives the remainder 9.6, not being thoroughly divided. So we will not write 5 and 9.6 on the list.

(vi) 48 ÷ 6 = 8

This division gives the remainder 0 and so is divisible by 8. So please put them 6 and 8 in your factor list.

1, 2, 3, 4, 6 …. 8, 12, 16, 24, 48

(vii) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

So 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 are factors of 48.

## Factor pairs of 48

1 x 48 = 48

2 x 24 = 48

3 x 16 = 48

4 x 12 = 48

6 x 8 = 48

So, (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8) are factor pairs of 48

## Factor pairs of -48

-1 x -48 = 48

-2 x -24 = 48

-3 x -16 = 48

-4 x -12 = 48

-6 x -8 = 48

So, (-1, -48), (-2, -24), (-3, -16), (-4, -12), and (-6, -8) are negative pair factors of 48

## Prime Factorization of 48

48 ÷ 2 = 24

24 ÷ 2 = 12

12 ÷ 2 = 6

6 ÷ 2 = 3

3 ÷ 3 = 1

Therefore, 2 × 2 × 2 × 2 × 3 are Prime factorization of 48.

## Factor tree of 48

```
48
/ \
2 24
/ \
2 12
/ \
2 6
/ \
2 3
```

Factors of 3 |

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